Facts and formulae

Question 1

Pythagoras’ Theorem

Answer 1

a squared = b squared + c squared

Question 2

Formula for trigonometry

Answer 2

SOHCAHTOA

Question 3

The angle of elevation is the angle you look…

Answer 3

Up through

Question 4

The angle of depression is the angle you look…

Answer 4

Down through

Question 5

Rules for drawing bearings…

Answer 5

A bearing is measured:

• from the north line
• in a clockwise direction
• is written as three figures

Question 6

The Sine Rule

Answer 6

a b c
—– = —– = —–
sinA sinB sinC

And vice versa

Question 7

Finding a missing side with the cosine rule:

Answer 7

a squared = b squared + c squared - 2bccosA

You need two sides and the included angle

Question 8

Finding the missing angle with the cosine rule

Answer 8

cosA=b squared + c squared - a squared
———————————–
2bc

Question 9

Area of a triangle with the perpendicular height

Answer 9

A=1/2bh

Question 10

Area of a triangle without the perpendicular height

Answer 10

A=1/2absinC

Two sides and the angle included between them

Question 11

How do you square a bracket with two terms?

Answer 11

1) Square the first
2) Twice the product of the two numbers
3) Square the last

Question 12

What is a common exam question on T4 for four term factorising?

Answer 12

A question which involves using product and sum to go from three terms to four

Question 13

Quadratic formula

Answer 13

X= - b + or - the square root of b squared minus 4ac all over 2a
For ax squared + bx + c = 0

Question 14

Calculating the area of a sector

Answer 14

Asector = (theta/360) x pie r squared

Question 15

Finding the arc length

Answer 15

LengthAB = (theta/360) x pie d

Question 16

Finding the perimeter of a sector

Answer 16

P = 2r + LengthAB

Question 17

Area for a square/rectangle

Answer 17

A = l x b

Question 18

Area for a trapezium

Answer 18

A = 1/2(a + b)h

Question 19

Area for a parallelogram

Answer 19

A = b x perpendicular h

Question 20

Area for a triangle

Answer 20

A = 1/2bh

Or A = 1/2absinC (two sides and an included angle)

Question 21

Area for a circle

Answer 21

A = pie r squared

Question 22

Finding the circumference of a circle

Answer 22

C = pie d

Question 23

Volume of a prism

Answer 23

Volume of a prism = cross-sectional area x length

V = csa x l

Question 24

Volume of a cylinder

Answer 24

V = pie r squared h

Question 25

Surface area of a cylinder

Answer 25

Curved surface area of a cylinder = 2 pie rh

Area of a circle = pie r squared (then multiply this by two)

Question 26

Volume of a sphere

Answer 26

V = 4/3pie r cubed

Question 27

Surface area of a sphere

Answer 27

Surface area of a sphere = 4pie r squared (formula sheet)

Question 28

Volume of a cone

Answer 28

Volume of a cone = 1/3pie r squared h

h = perpendicular height of the cone - not the slant height

Question 29

Surface area of a cone

Answer 29

Curved surface area of a cone = pie r l (l is the slanted height of the cone)
Area of a circle = pie r squared